US7797105B2 - System and method for GPS acquisition using advanced tight coupling - Google Patents
System and method for GPS acquisition using advanced tight coupling Download PDFInfo
- Publication number
- US7797105B2 US7797105B2 US12/193,449 US19344908A US7797105B2 US 7797105 B2 US7797105 B2 US 7797105B2 US 19344908 A US19344908 A US 19344908A US 7797105 B2 US7797105 B2 US 7797105B2
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- Prior art keywords
- receiver
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Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
- G01S19/47—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being an inertial measurement, e.g. tightly coupled inertial
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/52—Determining velocity
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/53—Determining attitude
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- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Position Fixing By Use Of Radio Waves (AREA)
- Navigation (AREA)
Abstract
Description
I P =A d R(ρe)cos(θe)+ηP
Q P =A d R(ρe)sin(θe)+εP
I E =A d R(ρe −b/2)cos(θe)+ηE
Q E =A d R(ρe −b/2)sin(θe)+εE
I L =A d R(ρe +b/2)cos(θe)+ηL
Q L =A d R(ρe +b/2)sin(θe)+εL
-
- where:
- R(ρe)=max[1−(|ρe|/b),0],
- b=code chip in meters (=29.3 m for P code),
- A=amplitude, different for L1 and L2,
- d=BPSK navigation data bit, constant for 20 ms,
- ρe=residual (measurement−estimate) range error, meters,
- θe=L1 residual phase error, radians−different for L2
- η,ε=additive, white, Gaussian noise, zero-mean, variance σI,Q 2.
σELS=σIQ/√{square root over (20)}
IP , Q P , I PO , Q PO with noise variance σPS=σIQ/√{square root over (10)}
E(ξ)=0
E(ξ2)=8σELS 4+4A 2 σELS 2 F(ρe)
F(ρe)=2 ρe 2 /b 2+½ (2)
Since ½≦F(ρe)≦1, a relatively conservative estimate is F(ρe)=1
Y RR ≈−A 2 R 2(ρe){dot over (θ)}e (Δt/2)+γ (3)
E(γ)=0
E(γ2)=2σPS 4+2 A 2 R 2(ρe)σPS 2 (4)
for |ρe |≦b/2, 0.25≦R 2(ρe)≦1.
Residual range error=true range−estimated range=ρe=(λ/2π)θe (5)
Residual range rate error=true range rate−estimated range rate={dot over (ρ)}e=(λ/2π){dot over (θ)}e (6)
X=[θ e{dot over (θ)}e{umlaut over (θ)}e]T
where θe=measured phase−navigation estimated phase for the GPS L1 frequency.
{umlaut over (θ)}{umlaut over (θe)}=constant
X(t i)=F•X(t i−1)
-
- where:
- F=Identity(3,3) and
- F(1,2)=F(2,3)=Δt, F(1,3)=Δt2/2
- Δt=ti−ti−1
- where:
Y(t i)=[Y R(f 1) Y RR(f 1) Y R(f 2) Y RR(f 2)]T
where:
-
- YR and YRR are defined by equations (1) and (3), and
- f1 and f2 represent GPS L1 (1575.42 MHz) and L2 (1227.6 MHz).
Y(t i)=H•X (t i)+Γ(t i)
where:
- Γ(ti)=[ξ1 γ1 ξ2 γ2]T, the first and second noise pairs correspond to L1 and L2,
- H=Zeroes (4,3), and
- H(1,1)=(2A1 2/b)•(λ/2π),
- H(2,2)=−A1 2R2({circumflex over (ρ)}e)•Δt/2
- H(3,1)=(2A2 2/b)•(λ/2π),
- H(4,2)=−A2 2R2({circumflex over (ρ)}e)•Δt/2•(f2/f1),
- A1 and A2 correspond to I and Q amplitudes for L1 and L2 channels respectively, and
- {circumflex over (ρ)}e represents the present best estimate of ρe
R(t i)=E(ΓΓT)
where:
-
- R is diagonal since the noise terms are not correlated with each other,
- R(1,1), R(3,3)=equation (2) for L1 and L2 respectively, and
- R(2,2), R(4,4)=equation (4) for L1 and L2 respectively.
-
- σIQ 2=variance of the additive noise on the Is and Qs
- A1 and A2=I and Q amplitudes for L1 and L2
Y
Eres = sqrt[diag(H · · HT + R)] | ||
for i = 1,4 |
if |Y(ti) − (ti)| ≧ kres · Erers |
H(i,i) = 0 Do not process the ith measurement |
end |
end | ||
K(t i)=P(
{circumflex over (X)}(
{circumflex over (P)}(t i)=[I−K(t i)•H]•P(
In the above equation, I is the identity matrix.
X(
-
- Q (3×3)—represents state noise (usually set to zero to assure maximum smoothing of the measurement noise.
i=i+1
- Q (3×3)—represents state noise (usually set to zero to assure maximum smoothing of the measurement noise.
DR=(λ/2π)•{circumflex over (X)}(1), σDR 2=(λ/2π)2 •{circumflex over (P)}(1,1)
DRR=(λ/2π)•{circumflex over (X)}(2), σDRR 2=(λ/2π)2 •{circumflex over (P)}(2,2)
-
- where
- E(β)=0
- E(β2)=σAM 2=8•σELS 2(2•σELS 2+A2)
-
- State:
- a2=satellite signal amplitude squared, assumed constant
- State Model:
ai+1 2 =a i 2 +q i E(q i)=0, E(q i 2)=QE i
-
- Where G is the total gain from the GPS antenna, through the RF chain, to I and Q generation. Typically G is known to less than 2 dB.
KE(t i)=
{circumflex over (P)}E(t i)=[1−KE(t i)•G i 2 ]•PE
a 2(
-
- where
- η(i, j),ε(i, j) represents noise on the Is and Qs
- for the ith satellite at time tj
σIQ 2=α•σIQ 2+(1−α)•σIQ 2(t j) where (1−α)=1/N
A i =I i 2 +Q i 2
D i=[Δρ(I i−1 , I i+1 , Q i−1 ,Q i+1),Δ{dot over (ρ)}(I i ,Q i)]
where Δρ and Δ{dot over (ρ)} are the filter states as described above. For Am=Max(Ai), and a spacing of ½ chip between each tap:
Thus, the satellite range residual for tap m is Offsetm+Δρm and the satellite range rate residual for tap m is Δ{dot over (ρ)}m.
Claims (14)
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US11/413,632 US7415354B2 (en) | 2006-04-28 | 2006-04-28 | System and method for GPS acquisition using advanced tight coupling |
US12/193,449 US7797105B2 (en) | 2006-04-28 | 2008-08-18 | System and method for GPS acquisition using advanced tight coupling |
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US20090096671A1 (en) * | 2007-10-10 | 2009-04-16 | Seiko Epson Corporation | Positioning method, program, positioning device, and electronic apparatus |
US7924219B2 (en) * | 2007-10-10 | 2011-04-12 | Seiko Epson Corporation | Positioning method, program, positioning device, and electronic apparatus |
US8972166B2 (en) | 2012-07-17 | 2015-03-03 | Lockheed Martin Corporation | Proactive mitigation of navigational uncertainty |
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US7415354B2 (en) | 2008-08-19 |
US20080309552A1 (en) | 2008-12-18 |
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